+0

# Help with NT

0
349
1
+211

If 554b is the base b representation of the square of the number whose base b representation is 24b, then find b.

May 28, 2018

$$5b^2+5b+4 = (2b+4)^2\\ 5b^2+5b+4=4b^2+16b+16\\ b^2-11b-12=0\\ (b-12)(b+1)=0\\ b=12 \text{ or } b=-1\text{(rejected)}\\ \therefore b = 12$$